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Bootstrap misspecification tests for ARCH based on the empirical process of squared residuals. (English) Zbl 1060.62097
Summary: We propose and study by means of simulations and graphical tools a class of goodness-of-fit tests for ARCH models. The tests are based on the empirical distribution function of squared residuals and smooth (parametric) bootstrap. We examine empirical size and power by means of a simulation study. While the tests have overall correct size, their power strongly depends on the type of alternative and is particularly high when the assumption of Gaussian innovations is violated. As an example, the tests are applied to returns on Foreign Exchange rates.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C60 Computational problems in statistics (MSC2010)
62G09 Nonparametric statistical resampling methods
62-09 Graphical methods in statistics (MSC2010)
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